Understanding Motion and Physics Fundamentals

• Physics is concerned with the basic principles that describe how the universe works
• Physics deals with matter, motion, force, and energy

Physics Areas of Study

• Classical mechanics
• Waves and sounds
• Thermodynamics
• Electromagnetism
• Quantum mechanics
• Atomic and nuclear physics
• Relativity

Motion

• Motion is everywhere
• This chapter will discuss speed, velocity and acceleration
• Two basic kinds of motion exist: straight line and circular

Defining Motion

• Position is the location of an object
• A reference point must be given in order to define the position of an object
• Motion is when an object is undergoing a continuous change in position
• Description of motion is the time rate of change of position
• A combination of length and time describes motion

Velocity

• Speed and velocity have different meanings in Physical Science
• Speed is a scalar quantity, and is only magnitude (A car going 80 km/h)
• Velocity is a vector, and has both magnitude and direction (A car going 80 km/h north)
• Vector quantities may be represented by arrows
• The length of the arrow is proportional to magnitude
• Vectors may be both positive and negative

Speed

• Average Speed = distance traveled/time to travel distance
• The formula for average speed is v = d/t or v = Δd/Δt
• ∆ means 'change in'
• Over the entire time interval, speed is an average
• Distance is the actual path length traveled
• Instantaneous Speed is the speed of an object at an instance of time, with ∆t defined as very small
• Glance at a speedometer to determine instantaneous speed

Velocity

• Velocity is similar to speed except a direction is involved
• Average velocity is displacement divided by total travel time
• Displacement is the straight line distance between the initial and final position with direction toward the final position
• Instantaneous velocity is similar to instantaneous speed except it has direction

Constant Velocity Example

• A car travels 20m every second
• The car, after 4 seconds, will have traveled 80m
• Given this, d = 80 m and t = 4.0 s
• The formula used to calculate this is v = d/t
• d/t = 80 m/4.0 s = 20 m/s = average speed
• Velocity would be described as 20 m/s in the direction of motion (east?)

Constant Velocity Confidence Exercise

• To calculate how far the above car would travel in 10s: v = d/t; vt = d; (20 m/s) (10 s) = 200 m

Sunlight Example

• The formula to calculate how long it takes sunlight to reach Earth is:
• Speed of light = 3.00 x 108 m/s = (v)
• Distance to earth = 1.50 x 108 km = (d)
• Use the formula: v = d/t and solve for t t = d/v
• t = d/v = 1.50 x 10^11 m/3.00 x 108 m/s
• t = 0.500 x 103 s = 5.00 x 102 s = 500 seconds

Earth's Orbit

• To determine the average speed in mi/h of the earth revolving around the sun, you have to use the formulas
• t = 365 days (must convert to hours)
• t = 365 days x (24h/day) = 8760 h
• Earth's radius (r) = 9.30 x 107 miles
• Given Radius you can then calculate the Distance
• A circle's circumference = 2nr and d = 2tr = 2 (3.14) (9.30 x 107 mi)
• Can then solve the equation: d/t = 2 (3.14) (9.30 x 107 mi) / 8760 h = 0.00667 x 107 mi/h
• v = avg. velocity = 6.67 x 104 mi/h = 66,700 mi/h

Earth and the Equator

• To calculate average speed in mi/h of a person at the equator as a result of the Earth's rotation, you have to use the formulas
• Radius of the Earth = RE = 4000 mi
• Time = 24 h
• Diameter of Earth = 2tr = 2 (3.14) (4000mi) = 25,120 mi
• v = d/t = (25,120 mi)/24h = 1047 mi/h

Acceleration

• Changes in velocity occur three ways: increase in magnitude, decrease in magnitude, change direction of velocity vector
• Any of these changes mean the object is accelerating
• Faster the change ☐ Greater the acceleration
• Acceleration is the time rate of change of velocity

Acceleration Measured

• Acceleration is a measure of the change in velocity during a given time period change in velocity divided by time for change to occur
• Avg. acceleration is Δν V-V 1-o
• a = — = — (vf= final & vo = original) t t
• Units of acceleration are = (m/s)/s = m/s²
• Only constant acceleration is considered

9•8 m/s² Velocity and Falling

• As the velocity increases, the distance traveled by the falling object increases each second

Finding Acceleration Example From Rest

• A car moving from rest accelerates along a track and reaches 90km/h in 7 sec
• To calculate the acceleration given
• vo = is 0, v₁ = 90 km/h, and t=7.0s
• the acceleration units must be in m/s2
• Therefore converting to m/s from km/h is Vf =90 km/h x (.278 m/s /km/h) =25 m/s
• a =Vf - Vo/t = 25 m/s - 0 / 7.0 = 3.57 /m/s2

Formula to Rearrange and Compute Final Velocity

Vf= Vo+at

Finding Acceleration

• If the car found on a previous example continues to accelerate t the sale rate for three more seconds what will it's velocity at the end
• The variables are a is 3.57 m/s2, and t= 10s
• The use of the equation Vf= Vo+at with Vf= 0 + (3.57s) x ( 10s) = 35.7m/s

Vectors and Acceleration

• Acceleration is a vector quantity since velocity is a vector quantity

Constant Acceleration Gravity

• Constant Acceleration Gravity = 9.8 m/s²
• A special case is associated with falling objects
• Vector towards the center of the earth
• Denoted by "g”
• = 9.80 m/s²

Velocity Due to Gravity

• Distance Formula d= 1/2 gt2
• This equation computes the distance (d) an object drops due to gravity (neglecting air resistance) in a given time (t)

Solving the Distance Via Example

• A ball dropped from a tall building = a distance travelled in how far from 1.50sec.s
• If g (gravity) = 9.80/m/s2 , and t= 1.5 (time) then to calculate the gravity we do
• d= 1/2 gt2 ===1/2 of (9. 80/sec/squared) x (1.5sec) = .1.10m for total distance the ball will travel

Final Speed Confidence to Measure Final Speed

• A= g=9.80 /sec( squared) , time is 1.,5 sec
• So the calculations used for the formula of v_f= at = (9.80 m/s²)(1.5 s)
• The Speed of ball after 1.5 seconds = 14.7 m/s
• Constant Acceleration = Gravity 9.8 m/s²
• Distance is proportional to t² (d = 1/2 gt²)
• Velocity is proportional to t - (vf = at)
• Acceleration due to gravity occurs in BOTH directions:
• Going up (-)
• Coming down (+)
• The ball returns to its starting point with the same speed it had initially
• vf

Acceleration in Uniform Circular Motion

• Although an object in uniform circular motion has a constant speed, it is constantly changing directions and therefore its velocity is constantly changing directions.
• Since there is a change in direction there is a change in acceleration.
• this acceleration? it is at right angles to the velocity and generally points toward the center of the circle

Acceleration in Uniform Circluar Motion in Action

• The acceleration supplied by friction of tires = car acceleration
• The car remains in a circular path as long as there is enough centripetal acceleration

Centripetal Acceleration Defined

V2

ac = r

• This equation holds true for an object moving in a circle with radius (r) and constant speed (v).
• From the equation we see that centripetal acceleration increases as the square of the speed.
• We also can see that as the radius decreases, the centripetal acceleration increases.

Important Equations

• v = d/t (average speed)
• d = 1/2at² (distance traveled, starting from rest)
• d = 1/2gt² (distance traveled, dropped object)
• a = vf Vo (constant acceleration)
• — t
• g = 9.80 m/s² = 32 ft/s² (acceleration, near Earth's surface, due to gravity) gravity)t at (final velocity with constant a)
• ac = v²/r (centripetal acceleration)
• a = g=9.80/sec (squared or constant)
• We are studying projectile motion and it's relation with air resistance
• With a combination of straight line and vertical notion of how independently one action works vs another
• With air resistance a horizonal projection with constance velocity = the rate of gravity in terms of falling
• Projected at an Angel (not horizontal) and the range of horizonal velocity

Air resistance

• In throwing a football the horizontal velocity remains constant but the vertical velocity changes like that of an object thrown upward
• If air resistance is neglected, projectiles have symmetric paths andthe maximum range is attained at 45°
• Under real-world conditions, air resistance causes the paths to be non-symmetric/ air resitance reduces the horizontal velocity
• Projectiles - Athletic considerations
• angle and speed of ball
• wind/directions / weather and altitude

Object Horizontally

• horizontally will fall at the same tate as its vertical counterpart
• and do not affect speed or vertical acceleration